Pre-Algebra Examples

$a^{2} - 6 a + 9 = 0$

Step 1

Factor using the perfect square rule.

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Step 1.1

Rewrite $9$ as $3^{2}$ .

$a^{2} - 6 a + 3^{2} = 0$

Step 1.2

Check that the middle term is two times the product of the numbers being squared in the first term and third term.

$6 a = 2 \cdot a \cdot 3$

Step 1.3

Rewrite the polynomial.

$a^{2} - 2 \cdot a \cdot 3 + 3^{2} = 0$

Step 1.4

Factor using the perfect square trinomial rule $a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$ , where $a = a$ and $b = 3$ .

${(a - 3)}^{2} = 0$

Step 2

Set the $a - 3$ equal to $0$ .

$a - 3 = 0$

Step 3

Add $3$ to both sides of the equation.

$a = 3$